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We define the cluster algebra associated with the Q-system for the Kirillov-Reshetikhin characters of the quantum affine algebra $U_q(\hat{\g})$ for any simple Lie algebra g, generalizing the simply-laced case treated in [Kedem 2007].
A. N. Kirillov and N. Yu. Reshetikhin, Formulas for the multiplicities of the occurrence of irreducible components in the tensor product of representations of simple Lie algebras , Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 205
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Atsuo Kuniba, Tomoki Nakanishi, and Junji Suzuki, Functional relations in solvable lattice models. I. Functional relations and representation theory , Internat. J. Modern Phys. A 9
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Vyjayanthi Chari and Andrew Pressley, A Guide to Quantum Groups , Cambridge University Press, Cambridge, 1995
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E. Frenkel and N. Reshetikhin, The q q -characters of representations of quantum affine algebras and deformations of W W -algebras
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G. Hatayama, A. Kuniba, M. Okado, T. Takagi, and Y. Yamada, Remarks on fermionic formula , Recent developments in quantum affine algebras and related topics (Raleigh, NC, 1998), Contemp. Math., vol. 248, Amer. Math. Soc., Providence, RI, 1999, pp. 243–291
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Sergey Fomin and Andrei Zelevinsky, Cluster algebras. I. Foundations , J. Amer. Math. Soc. 15
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Goro Hatayama, Atsuo Kuniba, Masato Okado, Taichiro Takagi, and Zengo Tsuboi, Paths, crystals and fermionic formulae , MathPhys Odyssey, 2001, Prog. Math. Phys., vol. 23, Birkhäuser Boston, Boston, MA, 2002, pp. 205–272
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Atsuo Kuniba and Tomoki Nakanishi, Bethe equation at q = 0 q=0 , Möbius inversion formula, and weight multiplicities: II. X n X_{n} case , J. Algebra 251
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by same author, Y Y -systems and generalized associahedra , Ann. of Math. (2) 158
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Hiraku Nakajima, t t -analogs of q q -characters of Kirillov-Reshetikhin modules of quantum affine algebras , Represent. Theory 7
2003
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A.Berenstein, S.Fomin, A.Zelevinsky, Cluster algebras III: Upper bounds and double Bruhat cells Duke Math. J. 126
2005
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by same author, The Kirillov-Reshetikhin conjecture and solutions of T T -systems , J. Reine Angew. Math. 596
2006
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by same author, Cluster algebras. IV. Coefficients , Compos. Math. 143
2007
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C. Geiss, B.Leclerc, and J. Schröer, Rigid modules over preprojective algebras ii: The Kac-Moody case , arXiv:math/0703039 [math.RT]
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